A Faster and More Space-Efficient Algorithm for Inferring
Arc-Annotations of RNA Sequences through Alignment

JesperJansson,
See-Kiong Ng, Wing-Kin Sung and Hugo Willy

The nested arc-annotation of a sequence is an important model used to
represent structural information for RNA and protein sequences. Given two
sequences S1 and S2 and a nested arc-annotation P1
for S1, this paper considers the problem of inferring the nested
arc-annotation P2 for S2 such that (S1,P1) and (S2,P2) have the
largest common substructure. The problem has a direct application in predicting
the secondary structure of an RNA sequence given a closely related sequence
with known secondary structure. The currently most efficient algorithm for this
problem requires O(nm3) time and O(nm2)
space where n is the length of the sequence with known arc-annotation and m is
the length of the sequence whose arc-annotation is to be inferred. By using sparsification on a new recursive dynamic programming algorithm
and applying a Hirschberg-like traceback technique
with compression, we obtain an improved algorithm that runs in min{O(nm2+n2m),O(nm2
log n), O(nm3)} time and min{O(m2 + mn),
O(m2 log n+n)} space.